Roundoff noise and overflow in normal digital filters

Minimum-norm realizations of fixed-point digital filters provide guaranteed immunity from autonomous overflow limit cycles. This paper presents an analysis of the relationship between dynamic range and roundoff noise for a class of minimum-norm realizations called "normal." For normal realizations, the eigenvectors of the system matrix form an orthogonal basis for the system state space. An explicit expression for minimum roundoff noise, under an 12 dynamic range constraint, is derived, and means for achieving this minimum are given. The simple expression for minimum roundoff noise permits easy determination, by trial and error, of optimal subfilter structures. Explicit expressions for the state-space parameters of optimal secondorder normal filters are given.